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The US is, however, learning exactly what happens when rationality is not part of the equation. This is all a dance around what is a "fact" and how to string facts into a reasoning model that lets you predict or confirm other potential facts, etc...

It's simply different people we're talking about. Certain personalities are always going to gravitate to the "search for reason" model in life rather than "reason about facts".

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At least in the field of sports science and exercise physiology, we have very little in the way of facts. Much of what we once thought were facts have been disproven or at least called into question by later research. So we need to be humble, and very circumspect in what we label as a "fact".
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Yeah, so much of this is not about facts as much as judgment: knowing what are the most themes and factors to making a system work well. What are the parts that, if you get right, everything else will follow. Knowing what areas it's okay, even beneficial, to rediscover instead of trying to plan ahead of time.
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Do you have any go-to examples of “facts” that were disproven in this field?
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Zone 2 training is a good use of time for amateur endurance athletes.

https://www.youtube.com/watch?v=QQnc6-z7AO8

Post exercise muscle soreness is caused by lactic acid buildup.

https://my.clevelandclinic.org/health/body/24521-lactic-acid

Icing is an effective treatment for minor musculoskeletal injuries.

https://www.yalemedicine.org/news/rice-protocol-for-injuries

Weight training for children will stunt their growth.

https://peterattiamd.com/belindabeck/

Stretching before exercise prevents injuries.

https://mcpress.mayoclinic.org/nutrition-fitness/does-stretc...

I could go on and on but I think you get the point. Almost everything you hear in this field is opinions, extrapolations, and educated guesses rather than anything we could really call a "fact".

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Like what? There are some basics that have been studied and represent useful approximations. The general statement that your body "makes specific adaptations to imposed demands" seems to hold no matter what you do. There seems to always be some debate about what demands to impose to get a specific adaptation. For example, people have a very diverse array of opinions about how and when to stretch to achieve certain kinds of flexibility and if you do some reading you will find that these opinions follow from a body of work in a specific activity and that they don't always translate well to other activities.
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